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Statistical Voltage Quality Evaluation of Wind Farm-

connected Grid Network

Q. Li and Y. Yuan

Hohai University, [email protected]

S. S. Choi

Nanyang Technological [email protected]

W. S. Wang

China Electric Power Research [email protected]

AbstractA statistical approach is proposed in the assessment of

voltage quality of network interconnected to a wind-farm.

Random wind speed and uncertainty in the network status

contribute toward the stochastic nature of the voltage quality.

The analysis takes into consideration the reactive power

capability of wind turbine generators (WTG). Judicious

application of the reactive power control is shown to enhance the

voltage quality.

Keywords- Voltage quality, wind farm, reactive power capability.

I.

INTRODUCTION

As a promising renewable energy source, wind powergeneration is experiencing rapid development. By 2009, theglobal wind power installed capacity has amounted to some150 GW [1]. Unfortunately, due to the random nature of windspeed, output power from wind farm tends to be highlyunsteady. Thus integration of large-scale wind farm bringsabout many challenges for power system operator, in whichvoltage quality is the prominent one. Network voltage will varywith the fluctuations of the injected wind power, and the degreeof degradation in the voltage quality increases with the windpower injection level.

For the purpose of increasing the efficiency of wind energyutilization, variable speed WTG has been developed in whichdouble fed induction generator (DFIG) and permanentmagnetic synchronous generator (PMSG) are the mostprominent examples. Using variable speed control, maximumwind energy capture can be achieved while reactive power ofthe WTG can be controlled simultaneously. The reactive powercontrol strategy of the WTG can be used to improve networkvoltage quality [2].

This investigation begins with an examination of thereactive power capability of WTG and is followed by ananalysis on the impact of the WTG on voltage quality. Due tothe stochastic nature of the injected power from wind farm, a

statistical approach is considered appropriate in the evaluationof the voltage variations. Indeed, probabilistic load flow hasbeen used in [3, 4] to perform such an assessment. However,the process is tedious and requires high computation time. Analternative method has been proposed in [5] in which therandom injected wind power and the uncertain grid states areconsidered simultaneously. The distribution of voltagedeviation is determined. Unfortunately, the approach in [5]assumes a fixed power factor at the wind farm terminals andhas not taken full advantage of the wider range of the reactive

power capability of WTG in the wind farm. This aspect is to bestudied in detail in this investigation.

Although generally DFIG and PMSG have the ability toproduce/absorb reactive power, this reactive power capability isconstrained. As described in [6] and [7], the reactive powercapability of DFIG mainly depends on the maximum current ofrotor, grid-side convertor and active power level. On the otherhand, due to the fully-rated capacity of the convertor used inPMSG, the reactive power capability only depends on the grid-

side convertor and active power level [8]. These factors will beconsidered in detail in Section II. The method for statisticalvoltage deviation assessment is described in Section III, whichalso includes case study for verifying the proposed scheme.The results are analyzed in Section IV, and a method fordetermining the level of wind power penetration into gridsystem is presented. Main findings and conclusions are givenin Section V.

II.

REACTIVE POWER CAPABILITY OF WTG

With rapid development of power converter technologies,DFIG and PMSG have become most prominent in WTG.Unlike WTG based on fixed-speed induction generator, both

DFIG and PMSG have certain degree of reactive powerregulation ability. The voltage deviation at the terminals of theWTG can be regulated by controlling the injected reactivepower from the generators. However, both types of WTGs canonly generate reactive power within certain range in order notto shorten their useful life. Therefore, it is important to studyclosely the reactive power range of the two types of WTG, asfollows.

A.

Reactive Power Capability of DFIG

DFIG has been widely adopted in present-day wind farms.A DFIG is made up of an induction generator with amultiphase wound rotor and a multiphase slip ring assembly,with brushes for access to the rotor windings. The principle of

the DFIG is that rotor windings are connected to the grid viaslip rings and back-to-back convertor which is used to controlboth the rotor and the grid currents. By this means, rotorfrequency can freely differ from the grid frequency. By usingthe convertor to control the rotor currents, it is possible toadjust the active and reactive power fed to the grid from thestator independently of the generators rotational speed [9].

The reactive power of a DFIG is made up of two parts: thatfrom the stator and from the grid-side convertor. According to

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the analysis in [6] and [7], the active and reactive power of thestator side can be described by the following equations.

==

==

ss

sq

rdsq

s

msdsqs

rqsq

s

msqsqs

L

UIU

L

LIUQ

IUL

LIUP

2

3

2

3

2

3

2

3

2

3

2

(1)

where , are the active and reactive power output of WTGstator, respectively. , , and are the stator voltage and currentalong the q and d-axis components, respectively. , are therespective mutual- and the self-inductance of stator windings.is the angular synchronous speed.

Furthermore, the relationship between captured mechanicalpower and the stator active power is

s

PP ms

=

1 (2)

In (2), s denotes the slip of the generator. Also from (1),equation (3) can be determined:

222

2

2

3

2

3

=

++ rs

s

m

ss

sq

ss IUL

L

L

UQP

(3)

By combining (2) and (3), one obtains

2

max

222

2

3

2

3

1

++

rs

s

m

ss

sq

sm IU

L

L

L

UQ

s

P

(4)

where max is maximum permitted current on the rotor-side convertor. Assuming the maximum and minimum reactivepower from the stator of the WTG is and . Then the range thereactive power from the stator can be determined as:

22

max

2

min12

3

2

3

=

s

PIU

L

L

L

UQ mrs

s

m

ss

ss

(5)

22

max

2

max12

3

2

3

+=

s

PIU

L

L

L

UQ mrs

s

m

ss

ss

(6)

Under normal operation, the relationship between rotorpower and stator power is

sr sPP = (7)

Since the rotor is connected to the grid by the convertor,therefore the power of the grid-side convertor is the same to the

rotor power. Let the rated capacity of convertor be , thereforethe corresponding reactive power capability of the grid-sideconvertor is

22

rconcon PSQ = (8)

By combining (8) and (2), the reactive power capability ofthe rotor can be expressed as

2

2

min,1

=

s

sPSQ mconcon (9)

2

2

max,1

+=

s

sPSQ mconcon (10)

Thus the total reactive power that can be expected from the

DFIG is the sum of stator and the grid-side convertor

max,max,min,min consDtcons QQQQQ ++ (11)

B.

Reactive Power Capability of PMSG

As fully-rated capacity convertor is adopted for PMSG, theWTG is coupled to the grid by the convertor. Therefore, thereactive power capability only depends on the grid-sideconvertor and corresponding active power level.

Assuming the capacity of grid-side convertor is , and theactive power equals to the captured wind power , thecorresponding lower and upper limit of reactive powercapability are

22

min, mgg PSQ = (12)

22

max, mgg PSQ += (13)

Therefore, the reactive power capability of PMSG can bedetermined from

max,,min, gPtg QQQ (14)

According to (11) and (14), the reactive power capability ofthe WTG can be determined. Thus, the WTG reactive poweroperating range can be set within the respective range, with the

view to enhance voltage quality.

III.

STATISTICAL EVALUATION OF VOLTAGE DEVIATION

Due to the random injected wind power and grid statuswhich is likely to change with time, statistical method shouldbe adopted to evaluate voltage quality. The wind powerdistribution can be determined by the distribution of windspeed. As for the grid, different network status can beexpressed by different equivalent impedances. As is presentedin [5], the voltage deviation assessment can be achieved bycombining the wind power distribution and probability of thegrid Thevenin equivalence.

A.

Statistical Voltage Analysis for PCC with Reactive PowerCapability of WTG

Fig. 1 shows a wind farm inter-connected to a large gridsystem. In this figure, Z = R + jX represents the effectiveimpedance interconnecting the wind farm (shown by anaggregated WTG) and an infinite bus of constant voltage

01 . The voltage deviation at the Point-of-Common-Coupling (PCC) is of interest. The deviation depends on the

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injected wind power and the grid impedance, and (15) is oftenused to determine the bus voltage deviation.

V

QXPRV

+=

(15)

Where V is the voltage deviation at the PCC, Pand Q

are the injected power of PCC, V is the rated voltage of PCC.

Based on the method described in [5], the injected windpower and grid equivalent impedance can be treated as discretevariables at wind power state i and grid status j. Thus, thevoltage deviation of PCC can be calculated by (16). Detaileddescription can be found in [5].

V

jXiQjRiPjiV

)()()()(),(

+= (16)

= 01E

V

Fig. 1 Equivalent diagram of the wind power grid system

When the reactive power capability of WTG such as that

described by (11) or (14) is also considered, V can bereduced by adjusting Qt,P or Qt,D. If there is no limit on thereactive power, the desirable result is to maintain the voltage at

the PCC constant, i.e. V =0. However, both the DFIG and

PMSG can only operate with Q within specific range. From(16), for each given grid state, the WTG should generate the

reactive power Q within the permitted range to minimize V .Thus, for the given network state j and injected power P, Q areto be adjusted until the minimum V is obtained. This is theproposed reactive power regulation strategy of this paper.

In order to demonstrate the effectiveness of reactive powercapability of WTG to mitigate the voltage deviation at thePCC, an example is shown next. Parameters of the WTG canbe found in [10]. The statistical voltage deviation of PCC underfixed power factor and with the reactive power adjusted assuggested in this paper is presented. The statistical distributionof the grid Thevenin equivalence is that given in [5].

B.

Numerical Examples

1. Reactive Power Capability of WTG

As is discussed in Section II, the reactive power capabilityof a WTG depends on the parameters of wind turbine itself.Based on the WTG parameters presented in [10], the reactivepower capability of the WTG, assuming it is a DFIG, isillustrated in Fig. 2.

0 0.2 0.4 0.6 0.8 1.0

-1.0

-0.5

0

0.5

1.0

Active power / p.u.

Reactivepower/p.u.

Upper Limit

Lower Limit

Fig. 2 Reactive power capability of the DFIG considered in this example

0 0.2 0.4 0.6 0.8 1.0-1.00

-0.75

-0.50

-0.25

0

0.25

0.50

0.75

1.00

Active power / p.u.

Reac

tivePower/p.u.

Upper Limit

Lower Limit

Fig. 3 Reactive power capability of PMSG considered in this example

Different from the DFIG, the reactive power capability ofPMSG only depends on the capacity of grid-side inverter andthe active power level of WTG. Suppose the grid-sideconvertor equals to the rated capacity of active power, reactivepower capability is shown in Fig. 3.

2. Voltage Deviation Distribution with Fixed Power Factorat the PCC

Based on the wind power output and grid Theveninequivalence data presented in [5], the voltage fluctuation at thePCC can be determined. Fixed power factor has been adoptedas a possible mode of operation for WTG. For example, thestatistical voltage assessments at 0.98 and unity power factorconditions obtained in [5] are reproduced in Figures 4 and 5.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.20

0.05

0.1

0.15

0.2

0.25

Voltage deviation V

Probaili

ty

V>10%

Power Factor=0.98

Fig. 4 Voltage deviation distribution at the PCC under 0.98 PF condition

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0 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.200

0.05

0.10

0.15

0.20

0.25

0.30

0.35

Voltage Deviation V

Probability

V >10%

Power Factor = 1.0

Fig. 5 Voltage deviation distribution at the PCC under unity PF condition

3. Voltage Deviation Distribution with the Proposed

Reactive Power Strategy

Based on the proposed strategy on adjusting Q to minimizeV, the statistical voltage quality can be determined. Due to thedifference in the reactive power capability between the DFIGand PMSG, the voltage deviation is also different. They are

shown in Figures 6 and 8.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Voltage deviation

Probability

Fig. 6 Voltage deviation probability distribution for DFIG

Figure 6 shows the probability distribution of V using theDFIG WTG. The corresponding reactive power output of theDFIG is shown in Fig. 7. The corresponding results for thePMSG WTG are given in Figures 8 and 9.

0 0.2 0.4 0.6 0.8 1.0

-1.0

-0.5

0

0.5

1.0

Active power / p.u.

Reactiv

epower/p.u.

Upper Limit

Lower Limit

Optimal Result

Fig. 7 Reactive power capability of the DFIG which produces the voltagedeviation distribution shown on Fig. 6

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Voltage deviation

Probability

Fig. 8 Voltage deviation probability distribution with reactive power

capability of PMSG

0 0.2 0.4 0.6 0.8 1.0-1.00

-0.75

-0.50

-0.25

0

0.25

0.50

0.75

1.00

Active power / p.u.

ReactivePower/p.u.

Upper Limit

Lower Limit

Optimal Result

Fig. 9 Reactive power capability of the DFIG which produces the voltagedeviation distribution shown on Fig. 8

IV.

ANALYSIS OF THE RESULTS

A. Effectiveness of Reactive Power Capability for Voltage

Control

The effectiveness of the WTG reactive power control tominimize voltage deviation can be seen by comparing theresults obtained in [5] with that proposed in Section III.A.From the results of Fig. 4, 5, 6 and 8, it can be readily seen thatif the unity or 0.98 fixed power factor strategy is adopted, theprobability of larger than 10% is much larger than that if Q isadjusted within the WTG reactive power capability range. Notsurprisingly, the conclusion is that the reactive powercapability of the WTG should be effectively utilized tominimize the voltage deviation at the PCC. In fact, thestatistical voltage assessment has produced the voltagedeviation distribution so that it can provide useful informationon the extent of the voltage deviation caused by the integrationof wind farm.

B. Relationship between Wind Farm Capacity and Voltage

Control

The capacity of wind farm is a critical factor affecting thevoltage deviation at the PCC. The relationship between themcan be illustrated by examining Figure 10. In this figure, theprobability of


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varied according to the proposed method. Using this example,the figure shows that the probability of

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